1. ## Basis

I have no idea how to start solving this problem. My professor gives really bad notes. I know you guys dont like to work problems without the asker doing some work, but i dont know where to start. If someone could walk me through this i would greatly appreciate it.

I dont know how to format matrices so i just copied the problem from the website. Each set of numbers in parentheses should be in a 1 column matrix (top, bottom).

Any help is greatly appreciated.

Consider the basis of consisting of vectors
(-2, 5) and (-5, 4) .
Find in whose coordinate vector relative to the basis is
(-1, 6) .

2. You want to solve $\displaystyle a\left[ \begin{gathered} - 2 \hfill \\ 3 \hfill \\ \end{gathered} \right] + b\left[ \begin{gathered} - 5 \hfill \\ 4 \hfill \\ \end{gathered} \right] = \left[ \begin{gathered} - 1 \hfill \\ 6 \hfill \\ \end{gathered} \right]$

or $\displaystyle \left\{ \begin{gathered} - 2a - 5b = - 1 \hfill \\ 5a + 4b = 6 \hfill \\ \end{gathered} \right.$

3. I used substition and got a=26/17 and b=-7/17.

Is that my answer? Cause the website is telling me it's wrong.

4. Well the way you have formated the question makes it very hard to read.
I may not have understood what is being asked.

Do you do correctly?

5. Here's a screenshot of the question. It looked like you had understood it correctly.

6. See if this is what is meant by that wording.

7. Awesome! That worked. Could you explain how that works, cause i was certain that i was solving for an a and b like you had originally said.

8. Originally Posted by manofsteele888
Could you explain how that works, cause i was certain that i was solving for an a and b like you had originally said.
Well I am not sure I can.
The way that question is worded is missleading I think.
But I am not someone who regularly works with linear algebra wording.
Perhaps someone else here can explain that wording.

9. Ok, thanks man. Much appreciated.

10. Originally Posted by manofsteele888
I have no idea how to start solving this problem. My professor gives really bad notes. I know you guys dont like to work problems without the asker doing some work, but i dont know where to start. If someone could walk me through this i would greatly appreciate it.

I dont know how to format matrices so i just copied the problem from the website. Each set of numbers in parentheses should be in a 1 column matrix (top, bottom).

Any help is greatly appreciated.

Consider the basis of consisting of vectors
(-2, 5) and (-5, 4) .
Find in whose coordinate vector relative to the basis is
(-1, 6) .

.